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14 \title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
16 \author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
17 $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
24 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
25 use of its limited energy provision, so that it can fulfill its monitoring task
26 as long as possible. Among known available approaches that can be used to
27 improve power management, lifetime coverage optimization provides activity
28 scheduling which ensures sensing coverage while minimizing the energy cost. We propose such an approach called Perimeter-based Coverage Optimization
29 protocol (PeCO). It is a hybrid of centralized and distributed methods: the
30 region of interest is first subdivided into subregions and the protocol is then
31 distributed among sensor nodes in each subregion.
32 The novelty of our approach lies essentially in the formulation of a new
33 mathematical optimization model based on the perimeter coverage level to schedule
34 sensors' activities. Extensive simulation experiments demonstrate that PeCO can
35 offer longer lifetime coverage for WSNs in comparison with some other protocols.
37 \begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
43 \section{Introduction}
44 \label{sec:introduction}
46 The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
47 wireless communication hardware has given rise to the opportunity to use large
48 networks of tiny sensors, called Wireless Sensor Networks
49 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
50 tasks. A WSN consists of small low-powered sensors working together by
51 communicating with one another through multi-hop radio communications. Each node
52 can send the data it collects in its environment, thanks to its sensor, to the
53 user by means of sink nodes. The features of a WSN made it suitable for a wide
54 range of application in areas such as business, environment, health, industry,
55 military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
56 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
57 physical, chemical, or biological phenomena observed in the environment; a
58 processing unit which will process and store the collected measurements; a radio
59 communication unit for data transmission and receiving.
61 The energy needed by an active sensor node to perform sensing, processing, and
62 communication is supplied by a power supply which is a battery. This battery has
63 a limited energy provision and it may be unsuitable or impossible to replace or
64 recharge it in most applications. Therefore it is necessary to deploy WSN with
65 high density in order to increase reliability and to exploit node redundancy
66 thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
67 of sensing areas can be exploited to schedule alternatively some sensors in a
68 low power sleep mode and thus save energy. Overall, the main question that must
69 be answered is: how to extend the lifetime coverage of a WSN as long as possible
70 while ensuring a high level of coverage? These past few years many
71 energy-efficient mechanisms have been suggested to retain energy and extend the
72 lifetime of the WSNs~\citep{rault2014energy}.\\\\
73 This paper makes the following contributions.
75 \item We have devised a framework to schedule nodes to be activated alternatively such
76 that the network lifetime is prolonged while ensuring that a certain level of
77 coverage is preserved. A key idea in our framework is to exploit spatial and
78 temporal subdivision. On the one hand, the area of interest is divided into
79 several smaller subregions and, on the other hand, the time line is divided into
80 periods of equal length. In each subregion the sensor nodes will cooperatively
81 choose a leader which will schedule nodes' activities, and this grouping of
82 sensors is similar to typical cluster architecture.
83 \item We have proposed a new mathematical optimization model. Instead of trying to
84 cover a set of specified points/targets as in most of the methods proposed in
85 the literature, we formulate an integer program based on perimeter coverage of
86 each sensor. The model involves integer variables to capture the deviations
87 between the actual level of coverage and the required level. Hence, an
88 optimal schedule will be obtained by minimizing a weighted sum of these
90 \item We have conducted extensive simulation experiments, using the discrete event
91 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
92 our PeCO protocol to two approaches found in the literature:
93 DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
94 work published in~\citep{Idrees2} which is based on another optimization model
95 for sensor scheduling.
103 The rest of the paper is organized as follows. In the next section
104 some related work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
105 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
106 coverage model formulation which is used to schedule the activation of sensor
107 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
108 results and discusses the comparison with other approaches. Finally, concluding
109 remarks are drawn and some suggestions are given for future works in
110 Section~\ref{sec:Conclusion and Future Works}.
112 \section{Related Literature}
113 \label{sec:Literature Review}
115 In this section, some related works regarding the
116 coverage problem is summarized, and specific aspects of the PeCO protocol from the works presented in
117 the literature are presented.
119 The most discussed coverage problems in literature can be classified in three
120 categories~\citep{li2013survey} according to their respective monitoring
121 objective. Hence, area coverage \citep{Misra} means that every point inside a
122 fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
123 to the objective of coverage for a finite number of discrete points called
124 targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
125 preventing intruders from entering into the region of interest. In
126 \citep{Deng2012} authors transform the area coverage problem into the target
127 coverage one taking into account the intersection points among disks of sensors
128 nodes or between disk of sensor nodes and boundaries. In
129 \citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
130 sensors are sufficiently covered it will be the case for the whole area. They
131 provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
132 each sensor. $d$ denotes the maximum number of sensors that are
133 neighbors to a sensor, and $n$ is the total number of sensors in the
134 network. {\it In PeCO protocol, instead of determining the level of coverage of
135 a set of discrete points, our optimization model is based on checking the
136 perimeter-coverage of each sensor to activate a minimal number of sensors.}
138 The major approach to extend network lifetime while preserving coverage is to
139 divide/organize the sensors into a suitable number of set covers (disjoint or
140 non-disjoint)\citep{wang2011coverage}, where each set completely covers a region of interest, and to
141 activate these set covers successively. The network activity can be planned in
142 advance and scheduled for the entire network lifetime or organized in periods,
143 and the set of active sensor nodes is decided at the beginning of each period
144 \citep{ling2009energy}. Active node selection is determined based on the problem
145 requirements (e.g. area monitoring, connectivity, or power efficiency). For
146 instance, \citet{jaggi2006} address the problem of maximizing
147 the lifetime by dividing sensors into the maximum number of disjoint subsets
148 such that each subset can ensure both coverage and connectivity. A greedy
149 algorithm is applied once to solve this problem and the computed sets are
150 activated in succession to achieve the desired network lifetime.
151 \citet{chin2007}, \citet{yan2008design}, \citet{pc10}, propose algorithms
152 working in a periodic fashion where a cover set is computed at the beginning of
153 each period. {\it Motivated by these works, PeCO protocol works in periods,
154 where each period contains a preliminary phase for information exchange and
155 decisions, followed by a sensing phase where one cover set is in charge of the
158 Various centralized and distributed approaches, or even a mixing of these two
159 concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
160 own activity scheduling after an information exchange with its neighbors. The
161 main interest of such an approach is to avoid long range communications and thus
162 to reduce the energy dedicated to the communications. Unfortunately, since each
163 node has only information on its immediate neighbors (usually the one-hop ones)
164 it may make a bad decision leading to a global suboptimal solution. Conversely,
166 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
167 provide nearly or close to optimal solution since the algorithm has a global
168 view of the whole network. The disadvantage of a centralized method is obviously
169 its high cost in communications needed to transmit to a single node, the base
170 station which will globally schedule nodes' activities, and data from all the other
171 sensor nodes in the area. The price in communications can be huge since
172 long range communications will be needed. In fact the larger the WNS is, the
173 higher the communication and thus the energy cost are. {\it In order to be
174 suitable for large-scale networks, in the PeCO protocol, the area of interest
175 is divided into several smaller subregions, and in each one, a node called the
176 leader is in charge of selecting the active sensors for the current
177 period. Thus our protocol is scalable and is a globally distributed method,
178 whereas it is centralized in each subregion.}
180 Various coverage scheduling algorithms have been developed these past few years.
181 Many of them, dealing with the maximization of the number of cover sets, are
182 heuristics. These heuristics involve the construction of a cover set by
183 including in priority the sensor nodes which cover critical targets, that is to
184 say targets that are covered by the smallest number of sensors
185 \citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
186 programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
187 and dedicated techniques (solving with a branch-and-bound algorithm available in
188 optimization solver). The problem is formulated as an optimization problem
189 (maximization of the lifetime or number of cover sets) under target coverage and
190 energy constraints. Column generation techniques, well-known and widely
191 practiced techniques for solving linear programs with too many variables, have
193 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO
194 protocol, each leader, in charge of a subregion, solves an integer program
195 which has a twofold objective: minimize the overcoverage and the undercoverage
196 of the perimeter of each sensor.}
200 \section{ The P{\scshape e}CO Protocol Description}
201 \label{sec:The PeCO Protocol Description}
203 In this section, the Perimeter-based Coverage
204 Optimization protocol is decribed in details. First we present the assumptions we made and the models
205 we considered (in particular the perimeter coverage one), second we describe the
206 background idea of our protocol, and third we give the outline of the algorithm
207 executed by each node.
210 \subsection{Assumptions and Models}
213 A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
214 distributed in a bounded sensor field is considered. The wireless sensors are
215 deployed in high density to ensure initially a high coverage ratio of the area
216 of interest. We assume that all the sensor nodes are homogeneous in terms of
217 communication, sensing, and processing capabilities and heterogeneous from
218 the energy provision point of view. The location information is available to a
219 sensor node either through hardware such as embedded GPS or location discovery
220 algorithms. We assume that each sensor node can directly transmit its
221 measurements to a mobile sink node. For example, a sink can be an unmanned
222 aerial vehicle (UAV) flying regularly over the sensor field to collect
223 measurements from sensor nodes. A mobile sink node collects the measurements and
224 transmits them to the base station. We consider a Boolean disk coverage model,
225 which is the most widely used sensor coverage model in the literature, and all
226 sensor nodes have a constant sensing range $R_s$. Thus, all the space points
227 within a disk centered at a sensor with a radius equal to the sensing range are
228 said to be covered by this sensor. We also assume that the communication range
229 $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05}
230 proved that if the transmission range fulfills the previous hypothesis, the
231 complete coverage of a convex area implies connectivity among active nodes.
233 The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is
234 said to be perimeter covered if all the points on its perimeter are covered by
235 at least one sensor other than itself. Authors \citet{huang2005coverage} proved that a network area is
236 $k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
238 Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this
239 figure, sensor~$0$ has nine neighbors and we have reported on
240 its perimeter (the perimeter of the disk covered by the sensor) for each
241 neighbor the two points resulting from the intersection of the two sensing
242 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
243 for left and right from a neighboing point of view. The resulting couples of
244 intersection points subdivide the perimeter of sensor~$0$ into portions called
249 \begin{tabular}{@{}cr@{}}
250 \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
251 \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
253 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
254 $u$'s perimeter covered by $v$.}
258 Figure~\ref{figure1}(b) describes the geometric information used to find the
259 locations of the left and right points of an arc on the perimeter of a sensor
260 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
261 west side of sensor~$u$, with the following respective coordinates in the
262 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates
263 the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert
264 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
265 obtained through the formula:
267 \alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}
270 The arc on the perimeter of~$u$ defined by the angular interval $[\pi
271 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
273 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
274 in a counterclockwise manner, leading to a partitioning of the interval.
275 Figure~\ref{figure1}(a) illustrates the arcs for the nine neighbors of
276 sensor $0$ and Figure~\ref{figure2} gives the position of the corresponding arcs
277 in the interval $[0,2\pi)$. More precisely, the points are
278 ordered according to the measures of the angles defined by their respective
279 positions. The intersection points are then visited one after another, starting
280 from the first intersection point after point~zero, and the maximum level of
281 coverage is determined for each interval defined by two successive points. The
282 maximum level of coverage is equal to the number of overlapping arcs. For
284 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
285 (the value is highlighted in yellow at the bottom of Figure~\ref{figure2}), which
286 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
287 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
288 coverage and the sensor nodes covering the perimeter. The example discussed
289 above is thus given by the sixth line of the table.
294 \includegraphics[width=127.5mm]{figure2.eps}
295 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
303 \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
304 {\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
306 \begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
307 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
308 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
309 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
310 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
311 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
312 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
313 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
314 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
315 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
316 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
317 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
318 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
319 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
320 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
321 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
322 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
323 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
324 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
333 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
334 integer program based on coverage intervals. The formulation of the coverage
335 optimization problem is detailed in~Section~\ref{cp}. Note that when a sensor
336 node has a part of its sensing range outside the WSN sensing field, as in
337 Figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$
338 and the corresponding interval will not be taken into account by the
339 optimization algorithm.
344 \includegraphics[width=62.5mm]{figure3.eps}
345 \caption{Sensing range outside the WSN's area of interest.}
350 \subsection{The Main Idea}
352 The WSN area of interest is, in a first step, divided into regular
353 homogeneous subregions using a divide-and-conquer algorithm. In a second step
354 our protocol will be executed in a distributed way in each subregion
355 simultaneously to schedule nodes' activities for one sensing period.
357 As shown in Figure~\ref{figure4}, node activity scheduling is produced by our
358 protocol in a periodic manner. Each period is divided into 4 stages: Information
359 (INFO) Exchange, Leader Election, Decision (the result of an optimization
360 problem), and Sensing. For each period there is exactly one set cover
361 responsible for the sensing task. Protocols based on a periodic scheme, like
362 PeCO, are more robust against an unexpected node failure. On the one hand, if
363 a node failure is discovered before taking the decision, the corresponding sensor
364 node will not be considered by the optimization algorithm. On the other
365 hand, if the sensor failure happens after the decision, the sensing task of the
366 network will be temporarily affected: only during the period of sensing until a
367 new period starts, since a new set cover will take charge of the sensing task in
368 the next period. The energy consumption and some other constraints can easily be
369 taken into account since the sensors can update and then exchange their
370 information (including their residual energy) at the beginning of each period.
371 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
372 are energy consuming, even for nodes that will not join the set cover to monitor
377 \includegraphics[width=80mm]{figure4.eps}
378 \caption{PeCO protocol.}
382 We define two types of packets to be used by PeCO protocol:
385 \item INFO packet: sent by each sensor node to all the nodes inside a same
386 subregion for information exchange.
387 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
388 to transmit to them their respective status (stay Active or go Sleep) during
393 Five statuses are possible for a sensor node in the network:
396 \item LISTENING: waits for a decision (to be active or not);
397 \item COMPUTATION: executes the optimization algorithm as leader to
398 determine the activities scheduling;
399 \item ACTIVE: node is sensing;
400 \item SLEEP: node is turned off;
401 \item COMMUNICATION: transmits or receives packets.
405 \subsection{PeCO Protocol Algorithm}
407 The pseudocode implementing the protocol on a node is given below.
408 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
409 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
414 % \KwIn{all the parameters related to information exchange}
415 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
417 %\emph{Initialize the sensor node and determine it's position and subregion} \;
419 \noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
420 \hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
421 \hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
422 \hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
423 \hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
424 \hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
425 \hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
426 \hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
427 \hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
428 \hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
429 \hspace*{1.2cm} {\bf end}\\
430 \hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
431 \hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
432 \hspace*{1.2cm} {\bf end}\\
433 \hspace*{1.2cm} {\bf else}\\
434 \hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
435 \hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
436 \hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
437 \hspace*{1.2cm} {\bf end}\\
438 \hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
439 \hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
440 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
441 \hspace*{0.6cm} {\bf end}\\
442 \hspace*{0.6cm} {\bf else}\\
443 \hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
444 \hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
445 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
446 \hspace*{0.6cm} {\bf end}\\
449 \hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
456 In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
457 current number and the previous number of living nodes in the subnetwork of the
458 subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
459 must be greater than a threshold $E_{th}$ in order to participate in the current
460 period. Each sensor node determines its position and its subregion using an
461 embedded GPS or a location discovery algorithm. After that, all the sensors
462 collect position coordinates, remaining energy, sensor node ID, and the number
463 of their one-hop live neighbors during the information exchange. The sensors
464 inside a same region cooperate to elect a leader. The selection criteria for the
465 leader, in order of priority, are: larger numbers of neighbors, larger remaining
466 energy, and then in case of equality, larger index. Once chosen, the leader
467 collects information to formulate and solve the integer program which allows to
468 construct the set of active sensors in the sensing stage.
471 \section{Perimeter-based Coverage Problem Formulation}
474 In this section, the coverage model is mathematically formulated. The following
475 notations are used throughout the
477 First, the following sets:
479 \item $S$ represents the set of WSN sensor nodes;
480 \item $A \subseteq S $ is the subset of alive sensors;
481 \item $I_j$ designates the set of coverage intervals (CI) obtained for
484 $I_j$ refers to the set of coverage intervals which have been defined according
485 to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
486 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
487 in coverage interval~$i$ of sensor~$j$, that is:
491 1 & \mbox{if sensor $k$ is involved in the } \\
492 & \mbox{coverage interval $i$ of sensor $j$}, \\
493 0 & \mbox{otherwise.}\\
496 Note that $a^k_{ik}=1$ by definition of the interval.
498 Second, several binary and integer variables are defined. Hence, each binary
499 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
500 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
501 variable which measures the undercoverage for the coverage interval $i$
502 corresponding to sensor~$j$. In the same way, the overcoverage for the same
503 coverage interval is given by the variable $V^j_i$.
505 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
506 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
507 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
508 previous notations, the number of active sensors in the coverage interval $i$ of
509 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
510 lifetime, the objective is to activate a minimal number of sensors in each
511 period to ensure the desired coverage level. As the number of alive sensors
512 decreases, it becomes impossible to reach the desired level of coverage for all
513 coverage intervals. Therefore variables $M^j_i$ and $V^j_i$ are introduced as a measure
514 of the deviation between the desired number of active sensors in a coverage
515 interval and the effective number. And we try to minimize these deviations,
516 first to force the activation of a minimal number of sensors to ensure the
517 desired coverage level, and if the desired level cannot be completely satisfied,
518 to reach a coverage level as close as possible to the desired one.
523 Our coverage optimization problem can then be mathematically expressed as follows:
528 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
529 \textrm{subject to :}&\\
530 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i = l \quad \forall i \in I_j, \forall j \in S\\
531 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i = l \quad \forall i \in I_j, \forall j \in S\\
532 X_{k} \in \{0,1\}, \forall k \in A
537 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
538 relative importance of satisfying the associated level of coverage. For example,
539 weights associated with coverage intervals of a specified part of a region may
540 be given by a relatively larger magnitude than weights associated with another
541 region. This kind of integer program is inspired from the model developed for
542 brachytherapy treatment planning for optimizing dose distribution
543 \citep{0031-9155-44-1-012}. The integer program must be solved by the leader in
544 each subregion at the beginning of each sensing phase, whenever the environment
545 has changed (new leader, death of some sensors). Note that the number of
546 constraints in the model is constant (constraints of coverage expressed for all
547 sensors), whereas the number of variables $X_k$ decreases over periods, since
548 only alive sensors (sensors with enough energy to be alive during one
549 sensing phase) are considered in the model.
551 \section{Performance Evaluation and Analysis}
552 \label{sec:Simulation Results and Analysis}
555 \subsection{Simulation Settings}
558 The WSN area of interest is supposed to be divided into 16~regular subregions
559 and we use the same energy consumption model as in our previous work~\citep{Idrees2}.
560 Table~\ref{table3} gives the chosen parameters settings.
563 \tbl{Relevant parameters for network initialization \label{table3}}{
570 Parameter & Value \\ [0.5ex]
573 % inserts single horizontal line
574 Sensing field & $(50 \times 25)~m^2 $ \\
576 WSN size & 100, 150, 200, 250, and 300~nodes \\
578 Initial energy & in range 500-700~Joules \\
580 Sensing period & duration of 60 minutes \\
581 $E_{th}$ & 36~Joules\\
584 $\alpha^j_i$ & 0.6 \\
592 To obtain experimental results which are relevant, simulations with five
593 different node densities going from 100 to 300~nodes were performed considering
594 each time 25~randomly generated networks. The nodes are deployed on a field of
595 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
596 high coverage ratio. Each node has an initial energy level, in Joules, which is
597 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
598 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
599 node to stay active during one period, it will no longer participate in the
600 coverage task. This value corresponds to the energy needed by the sensing phase,
601 obtained by multiplying the energy consumed in the active state (9.72 mW) with the
602 time in seconds for one period (3600 seconds), and adding the energy for the
603 pre-sensing phases. According to the interval of initial energy, a sensor may
604 be active during at most 20 periods.
606 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
607 network coverage and a longer WSN lifetime. Higher priority is given to
608 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
609 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
610 sensor~$j$. On the other hand,
611 $\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
612 in covering the interval.
614 The following performance metrics are used to evaluate the efficiency of the
619 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
620 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
621 $Lifetime_{50}$ denote, respectively, the amount of time during which is
622 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
623 fulfill the expected monitoring task until all its nodes have depleted their
624 energy or if the network is no more connected. This last condition is crucial
625 because without network connectivity a sensor may not be able to send to a
626 base station an event it has sensed.
627 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
628 observe the area of interest. In our case, the sensor field is discretized as
629 a regular grid, which yields the following equation:
634 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
638 where $n$ is the number of covered grid points by active sensors of every
639 subregions during the current sensing phase and $N$ is total number of grid
640 points in the sensing field. In simulations a layout of
641 $N~=~51~\times~26~=~1326$~grid points is considered.
642 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
643 activate as few nodes as possible, in order to minimize the communication
644 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
649 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
652 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
653 current sensing period~$p$, $|J|$ is the number of sensors in the network, and
654 $R$ is the number of subregions.
655 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
656 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
657 divided by the number of periods. The value of EC is computed according to
662 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
663 + E^{a}_p+E^{s}_p \right)}{P},
666 where $P$ corresponds to the number of periods. The total energy consumed by
667 the sensors comes through taking into consideration four main energy
668 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
669 energy consumption spent by all the nodes for wireless communications during
670 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
671 the energy consumed by the sensors in LISTENING status before receiving the
672 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
673 refers to the energy needed by all the leader nodes to solve the integer
674 program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
675 consumed by the WSN during the sensing phase (active and sleeping nodes).
679 \subsection{Simulation Results}
681 In order to assess and analyze the performance of our protocol we have
682 implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two
683 other protocols, described in the next paragraph, will be evaluated for
684 comparison purposes. The simulations were run on a DELL laptop with an Intel
685 Core~i3~2370~M (1.8~GHz) processor (2 cores) whose MIPS (Million Instructions
686 Per Second) rate is equal to 35330. To be consistent with the use of a sensor
687 node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
688 equal to 6, the original execution time on the laptop is multiplied by 2944.2
689 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
690 Mathematical Programming (AMPL)~\citep{AMPL} is employed to generate the integer
691 program instance in a standard format, which is then read and solved by the
692 optimization solver GLPK (GNU linear Programming Kit available in the public
693 domain) \citep{glpk} through a Branch-and-Bound method.
695 As said previously, the PeCO is compared to three other approaches. The first
696 one, called DESK, is a fully distributed coverage algorithm proposed by
697 \citep{ChinhVu}. The second one, called GAF~\citep{xu2001geography}, consists in
698 dividing the monitoring area into fixed squares. Then, during the decision
699 phase, in each square, one sensor is chosen to remain active during the sensing
700 phase. The last one, the DiLCO protocol~\citep{Idrees2}, is an improved version
701 of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
702 PeCO and DiLCO protocols are based on the same framework. In particular, the
703 choice for the simulations of a partitioning in 16~subregions was made because
704 it corresponds to the configuration producing the best results for DiLCO. The
705 protocols are distinguished from one another by the formulation of the integer
706 program providing the set of sensors which have to be activated in each sensing
707 phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
708 whereas the PeCO protocol objective is to reach a desired level of coverage for each
709 sensor perimeter. In our experimentations, we chose a level of coverage equal to
712 \subsubsection{\bf Coverage Ratio}
714 Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
715 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
716 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
717 produced by PeCO for the first periods. This is due to the fact that at the
718 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
719 slightly decreases the coverage ratio), while the three other protocols activate
720 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
721 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
722 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
723 compared to DESK). The energy saved by PeCO in the early periods allows later a
724 substantial increase of the coverage performance.
729 \includegraphics[scale=0.5] {figure5.eps}
730 \caption{Coverage ratio for 200 deployed nodes.}
737 \subsubsection{\bf Active Sensors Ratio}
739 Having the less active sensor nodes in each period is essential to minimize the
740 energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6}
741 shows the average active nodes ratio for 200 deployed nodes. We observe that
742 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
743 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and
744 20.16~\% active nodes during the same time interval. As the number of periods
745 increases, PeCO protocol has a lower number of active nodes in comparison with
746 the three other approaches, while keeping a greater coverage ratio as shown in
747 Figure \ref{figure5}.
751 \includegraphics[scale=0.5]{figure6.eps}
752 \caption{Active sensors ratio for 200 deployed nodes.}
756 \subsubsection{\bf Energy Consumption}
758 We studied the effect of the energy consumed by the WSN during the communication,
759 computation, listening, active, and sleep status for different network densities
760 and compared it for the four approaches. Figures~\ref{figure7}(a) and (b)
761 illustrate the energy consumption for different network sizes and for
762 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
763 most competitive from the energy consumption point of view. As shown in both
764 figures, PeCO consumes much less energy than the three other methods. One might
765 think that the resolution of the integer program is too costly in energy, but
766 the results show that it is very beneficial to lose a bit of time in the
767 selection of sensors to activate. Indeed the optimization program allows to
768 reduce significantly the number of active sensors and so the energy consumption
769 while keeping a good coverage level.
773 \begin{tabular}{@{}cr@{}}
774 \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
775 \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
777 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
783 \subsubsection{\bf Network Lifetime}
785 We observe the superiority of PeCO and DiLCO protocols in comparison with the
786 two other approaches in prolonging the network lifetime. In
787 Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
788 different network sizes. As highlighted by these figures, the lifetime
789 increases with the size of the network, and it is clearly largest for DiLCO
790 and PeCO protocols. For instance, for a network of 300~sensors and coverage
791 ratio greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime
792 is about twice longer with PeCO compared to DESK protocol. The performance
793 difference is more obvious in Figure~\ref{figure8}(b) than in
794 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
795 time, and the lifetime with a coverage of 50\% is far longer than with
800 \begin{tabular}{@{}cr@{}}
801 \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
802 \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
804 \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
805 and (b)~$Lifetime_{50}$.}
811 Figure~\ref{figure9} compares the lifetime coverage of our protocols for
812 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
813 Protocol/90, and Protocol/95 the amount of time during which the network can
814 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
815 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
816 that do not require a 100\% coverage of the area to be monitored. PeCO might be
817 an interesting method since it achieves a good balance between a high level
818 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
819 lower coverage ratios, moreover the improvements grow with the network
820 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
821 not ineffective for the smallest network sizes.
824 \centering \includegraphics[scale=0.5]{figure9.eps}
825 \caption{Network lifetime for different coverage ratios.}
832 \section{Conclusion and Future Works}
833 \label{sec:Conclusion and Future Works}
835 In this paper we have studied the problem of Perimeter-based Coverage Optimization in
836 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
837 schedules nodes' activities (wake up and sleep stages) with the objective of
838 maintaining a good coverage ratio while maximizing the network lifetime. This
839 protocol is applied in a distributed way in regular subregions obtained after
840 partitioning the area of interest in a preliminary step. It works in periods and
841 is based on the resolution of an integer program to select the subset of sensors
842 operating in active status for each period. Our work is original in so far as it
843 proposes for the first time an integer program scheduling the activation of
844 sensors based on their perimeter coverage level, instead of using a set of
845 targets/points to be covered.
848 We have carried out several simulations to evaluate the proposed protocol. The
849 simulation results show that PeCO is more energy-efficient than other
850 approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
853 We plan to extend our framework so that the schedules are planned for multiple
856 We also want to improve our integer program to take into account heterogeneous
857 sensors from both energy and node characteristics point of views.
859 Finally, it would be interesting to implement our protocol using a
860 sensor-testbed to evaluate it in real world applications.
862 \bibliographystyle{gENO}
863 \bibliography{biblio}
